On swimming paramagnetic filaments

Under certain imposed magnetic field or flow conditions superparamagnetic beads can be coaxed into assembling into long filament structures. An intriguing variation on this occurs when the beads are pre-coated in primer, which binds to form a durable elastic link when two beads are brought into contact (\textitGoubault et al., PRL, \textbf91:260802). Curiously, when such a filament experiences a combination of applied uniform and oscillating magnetic fields it begins, slowly and reluctantly, to ``swim''. We argue that it is impossible for the filament to swim unless certain symmetries of the equations of motion are violated, and demonstrate that that this might occur either if there is a defect in one of the linkers or if the filament attains a metastable hairpin shape before the oscillating field is switched on. We show numerically and analytically how the bending stiffness can be backed out from the swimming speed, raising the possibility that simple measurements of swimming speed may allow us to experimentally assay the bond strength of the linking molecules